T2Test: Tamhane's T2 Post Hoc Test v2.2.0

In Analitica: Exploratory Data Analysis, Group Comparison Tools, and Other Procedures

Tamhane's T2 Post Hoc Test v2.2.0

Description

Performs the Tamhane T2 test for pairwise comparisons after an ANOVA model, assuming unequal variances and/or unequal sample sizes. This test is appropriate when the assumption of homogeneity of variances is violated, such as when Levene's test or Bartlett's test is significant.

Usage

T2Test(modelo, comparar = NULL, alpha = 0.05)

Arguments

modelo	An object of class aov or lm (full model: includes blocks, factors, etc.).
comparar	Character vector with the name(s) of the factor(s) to compare: - One name: main effect (e.g., "treatment" or "A") - Several names: interaction (e.g., c("A","B") for A:B) If omitted, it uses the first factor in modelo$xlevels.
alpha	Significance level (default is 0.05).

Details

The test uses a modified t-test with Welch-Satterthwaite degrees of freedom and a conservative approach to control for multiple comparisons.

Advantages: - Controls Type I error under heteroscedasticity. - No assumption of equal sample sizes.

Disadvantages: - Conservative; may reduce power. - Not as powerful as Games-Howell in some contexts.

Value

An object of class "tamhanet2" and "comparaciones", containing:

• Resultados: A data frame with pairwise comparisons, mean differences, t_value, gl, p_value, and significance codes.

• Promedios: A named numeric vector of group means as defined by comparar.

• Orden_Medias: Group names ordered from highest to lowest mean.

• Metodo: A character string indicating the method used ("Tamhane T2").

• Termino: The term being compared (e.g., "A", "B", or "A:B").

References

Tamhane, A. C. (1977). "Multiple comparisons in model I one-way ANOVA with unequal variances." Communications in Statistics - Theory and Methods, 6(1), 15–32. <https://doi.org/10.1080/03610927708827524>

Examples

data(d_e, package = "Analitica")
mod <- aov(Sueldo_actual ~ as.factor(labor), data = d_e)
resultado <- T2Test(mod)
summary(resultado)
plot(resultado)

# Con bloques, comparando solo el factor de interés
mod2 <- aov(Sueldo_actual ~ as.factor(labor) + Sexo, data = d_e)
res2 <- T2Test(mod2, comparar = "as.factor(labor)")
summary(res2)
plot(res2)

# Modelo con interacción
mod3 <- aov(Sueldo_actual ~ as.factor(labor) * Sexo, data = d_e)
res3 <- T2Test(mod3, comparar = c("as.factor(labor)", "Sexo"))
summary(res3)
plot(res3)

Analitica documentation built on Dec. 3, 2025, 9:07 a.m.